Abstract : This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing pattern mining with background knowledge, which has been a data mining issue for a long time. We propose encodings of the classical sequential pattern mining tasks within two representations of embeddings (fill-gaps vs skip-gaps) and for various kinds of patterns: frequent, constrained and condensed. We compare the computational performance of these encodings with each other to get a good insight into the efficiency of ASP encodings. The results show that the fill-gaps strategy is better on real problems due to lower memory consumption. Finally, compared to a constraint programming approach (CPSM), another declarative programming paradigm, our proposal showed comparable performance.